I am now a full-fledged member of the Internet generation: Hackers planted a virus on my computer last week and nearly stole my bank accounts.

This Zeus virus — named after the Greek god of all gods — is a mighty one, and a mighty tricky one.

Along with this column, I’m running a copy of the online statement of my bank accounts that thieves almost helped themselves to. (Forgive me for obscuring the numbers. I don’t want you to hurt yourself laughing.) Take a look at it, and I’ll explain what happened.

After I had logged onto Chase’s banking website to see my accounts, this screen popped up. So it was reasonable to assume at that point that the bank was trying to communicate with me.

And just so you don’t say, “Oh, I don’t bank with Chase so I’m OK,” Zeus is a notorious virus that doesn’t discriminate. Any account at any bank in any part of the world is vulnerable. So you might want to keep reading.

The pop-up screen sent out by the virus sat right on top of my account statement and locked up the legitimate Chase site underneath. And the way the pop-up screen was positioned kept me from getting to the Chase customer service number.

“In order to provide you with extra security, we occasionally need to ask for additional information when you access your accounts,” said Zeus, pretending to be Chase.

But there was something fishy — or phishy, as the computer geeks might say — about this, I thought immediately. Chase also wanted my driver’s license number. Why would Chase need that?

I closed out the site and quickly e-mailed someone I know at the bank. “Is there any reason Chase would be asking me these questions?”

The Chase guy had to make a call but the answer came back quickly: “No!”

Chase customer service helped me to quickly change my login name and password so that Zeus — which would have already transmitted both to the thieves by this time — couldn’t start snatching my money. (Chase also put an alert on its site because of my ordeal.) So I sit here today still a solvent man.

But some people aren’t so lucky.

“A small business could have a couple hundred thousand dollars or a million in the bank, and it could be wiped out instantly,” said one computer expert who, like everyone else, didn’t want his name used in this article.

Why request anonymity? Because the people who are using Zeus to steal money might make him and his company a target.

Zeus is so famous, as a matter of fact, that a cottage industry has been created around it over the past few years. Bad guys can buy variations of the virus and send them out from either a computer they own or someone else’s they’ve hacked.

ZeusTracker.com, which monitors the spread of Zeus around the globe, now lists 676 different computers (command and control servers, they’re called) that are sending out this particular virus.

Anti-virus software was catching only about one-third of the Zeus strains being sent out from places in Eastern Europe, Asia, South America and — yes — right here in the USA.

I still don’t know how my computer came to be infected, but I have a couple of suspicious e-mails that could have done the trick. Or I could have logged onto an infected site.

And since Zeus can be customized, don’t think the virus will look the same on your computer as it did on mine. Because the question on the driver’s license made me suspicious, I’m sure it won’t be on future versions of the virus.

Here’s the part of the story you might find the most interesting: The Zeus thieves apparently weren’t really interested in my money. It probably wasn’t a large enough amount for them.

What they really wanted was to steal my identity using the details they requested, including the Social Security number. If I had been foolish enough to give up those eight government-issued numbers, the crooks could have taken out loans and credit cards in my name.

Once they had my driver’s license, the thieves could have bought the Maserati I’ll never own. (At least I hope my thieves would have had that kind of exquisite taste.)

And they would have used the great credit rating I’ve built up over the decades in their evil plan.

(Incidentally, the folks at LifeLock, the company that sells products to fight identity theft, have been nice enough to keep a watch on all my accounts until the thieves decide to move on to other victims.)

You might remember a column I did last year about a Chinese food delivery guy copying my credit card details so he could use it to steal other people’s identities and buy $150 worth of volleyballs.

That’s chicken mei fun compared to the power of the Zeus virus.

But two instances of this nonsense in less than a year make me wonder if we should all go back to passbook savings accounts and Christmas clubs.